I couldn't post a review directly on Amazon so I'm going to post it here for anybody (graduate student or otherwise) that is taking a class that requires this book.

First of all, for some background, I'm a pure math major in my last year. I'm currently taking a graduate real analysis course, as well as 4 undergrad courses. One of these undergrad courses is called "Introduction to mathematical statistics". I decided to take it because I thought it would be a somewhat rigorous approach to a subject I never took any interest in.

Despite the plethora of rigor in my real analysis,differential geometry and differential topology classes, the textbook used ("Introduction to Mathematical Statistics and Data Analysis" by John Rice) guided the course to be not only the least rigorous out of all 5 I am taking this semester, but by far the least interesting and the most frustrating.

I don't mean to offend any stats majors because I haven't seen much of statistics (though I'm quite familiar with measure theory and the like), but the approach in this book is nowhere near rigorous. If this is mathematical statistics then 1st year physics is mathematical physics.

There are a LOT of examples in each chapter. Like a disturbing amount. Most of them were bland and boring without any context. The MATHEMATICS was seldom there. There might have been about 50 theorems in the book. This may be a bit selfish, but he labels many things as 'theorems' when they could easily pass off as propositions in 1st year analysis courses. A crapload of problems at the end of each chapter, almost all of them calculational.

In short, I did not see the motivation for approaching statistics from a theoretical point of view. Maybe that's not even possible. Fuck if I know. But what I do know is that this book just made it hell for me to actually learn some fucking statistics. It's littered with pretty graphs and pictures and long, useless formulas for distributions stated over and over. There is no abstract or theoretical approach: everything is calculational. It's disgusting.

In short, don't buy this book if you're looking for rigor. I have no idea of any of the other alternatives, but the book costs $250 and that is the biggest fucking ripoff of a textbook ever. Go buy a couple of PS3 games instead and you'll gain more utility out of them than this piece of trash.

The book is called "Introduction to Mathematical Statistics." I imagine a book called "Introduction to Mathematical Physics" [Edit: Or, even better, "Introduction to Mathematical Physics and Engineering", since I think it's fair to say Engineering:Physics::Data Analysis:Theoretical Statistics] would deal more with integrals and derivatives than tensor fields and novel algebras, would have "like a disturbing amount" of examples, fewer than 50 theorems, and many problems at the end of each chapter which were almost all calculational.

TL;DR: Of course it's not rigorous. The book isn't trash, you just had unreasonable expectations of an intro class/textbook.

I checked the preview, I guess it's on a page that's hidden. But yeah, no one is going to use this for a graduate course at least if they are mathematicians or statisticians, but I suppose grad students in fields which are weaker in math. Do art history majors need a grad text in mathematical statistics?

In the preface he said they do a rigorous proof of the CLT and LLN, but it was cut out. I sincerely wonder what he considers rigorous in this regard... mind posting his proof of the CLT.

That is a pretty strong assumption, but exactly what I'd do in an undergraduate math/stat class. A good 'rigorous' proof would be unnecesarily long and require a lot more math than you really want to delve into. Also, we wouldn't normally cover characteristic functions in undergrad math/stat, and you certainly wouldn't be covering levy's continuity theorem.

Edit: I don't know about your line on art history majors needing a grad text in stats, but to be honest, other grad stats texts aren't that rigorous either. I don't know what you're trying to say.

It was a joke about his book being inappropriate for grad students.

edit I think you need to keep in mind that the math stats courses are meant to give theoretical justification to methods while typically discussing many methods. If you want a very rigorous formalization, you can usually get that in a probability text.

In other words, I think you are expecting the wrong thing out of the math stat texts.

Alright. I haven't taken much probability theory so I haven't seen a proof of Levy's continuity theorem or characteristic functions. The biggest course I've taken related to probability theory is measure theory, which may not even be that related.

Why are you so mad? If it's easy for you, just pick up a real stats book, like Bikel and Doksum, or if its the lack of probability rigor, try Resnick's A probability path. Not everyone who wants to learn statistics and data analysis can get a degree in pure math. Examples and calculational problems help people understand how the machinery works if they aren't as familiar or practiced at reading and understanding equations.